We present on high- field electron spin resonance (ESR) studies of magnetic excitations in the spin- 1/2 triangular-lattice antiferromagnet Cs2CuBr4. Frequency- field diagrams of ESR excitations are measured for different orientations of magnetic fields up to 25 T. We show that the substantial zero- field energy gap, Δ ≈ 9.5 K, observed in the low-temperature excitation spectrum of Cs2CuBr4 [Zvyagin et al:, Phys. Rev. Lett. 112, 077206 (2014)], is present well above TN. Noticeably, the transition into the long-range magnetically ordered phase does not significantly affect the size of the gap, suggesting that even below TN the high-energy spin dynamics in Cs2CuBr4 is determined by short-range-order spin correlations. The experimental data are compared with results of model spin-wave-theory calculations for spin-1/2 triangle-lattice antiferromagnet.